Final answer:
The work done by a conservative force is related to the change in potential energy because it only depends on the initial and final positions, storing the energy as potential. Kinetic energy is accounted for separately in the work-energy theorem, which states that net work equals change in kinetic energy. With only conservative forces, mechanical energy is conserved, linking changes in potential energy to corresponding changes in kinetic energy.
Step-by-step explanation:
Work done by a conservative force is directly related to the change in potential energy because a conservative force, by definition, does not depend on the path taken, only on the initial and final positions. Conservative forces, such as gravity or the elastic force in a spring, store the work done as potential energy. When dealing with conservative forces and ignoring other forces like friction, the work-energy theorem indicates that the total mechanical energy (the sum of kinetic and potential energy) of a system remains constant.
The reason that work done by a conservative force does not account for changes in kinetic energy is because kinetic energy is accounted for separately in the work-energy theorem. This theorem states that the net work done on a system equals the change in its kinetic energy. So, when conservative forces are involved and no nonconservative forces do work, we can use the conservation of mechanical energy principle which states that the total mechanical energy (kinetic plus potential) of the system remains constant. This implies that any change in potential energy results in an equal but opposite change in kinetic energy, and vice versa.